1. Equations & Inequalities

When the sum of 1 and twice a negative number is subtracted from twice the square of the number, 0 results. Find the number.

Write a quadratic equation in general form whose solution set is {- 3, 5}.

Use specific values for x and y to show that, in general, 1/x + 1/y is not equivalent to 1 / x + y.

Solve each equation by the square root property. $\frac{x^2}{2}+5=-3$

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. $x^2+20x$

Solve each equation by completing the square. $3x^2-12x+11=0$

Solve each equation in Exercises 1 - 14 by factoring. 10x - 1 = (2x + 1)²

Determine the constant that should be added to the binomial so that it becomes a perfect square trinomial. Then write and factor the trinomial. x² - 10x

Solve each equation in Exercises 83–108 by the method of your choice. 2x/(x - 3) + 6/(x + 3) = - 28/(x² - 9)

Find all values of x satisfying the given conditions. y₁ = 2x/(x + 2), y₂ = 3/(x + 4), and y₁ + y₂ = 1

List all numbers that must be excluded from the domain of each rational expression. 3/(2x² + 4x - 9)

Solve each equation by the method of your choice. 1/(x² - 3x + 2) = 1/(x + 2) + 5/(x² - 4)

Solve each equation by the method of your choice. √2 x² + 3x - 2√2 = 0

Solve each equation in Exercises 83–108 by the method of your choice. 3/(x - 3) + 5/(x - 4) = (x² - 20)/(x² - 7x + 12)

Solve each equation in Exercises 15–34 by the square root property. (x + 2)² = 25